Find the number of units that produces maximum profit

Question

A company has a production cost function c(x)=12x+160 and a revenue function r(x)=-3x^2+180x when x units are sold. Find the number of units that produces maximum profit. Answer choices are:

less than 26

Between 26 and 29

between 29 and 32

between 32 and 35

more than 35

Answer 1

r'-c' = -6x+180- 12 = 0

6x = 168

x = 168/6 = 28

profit = r-c

take the derivative and set = 0, solve for x